Reflections and Translations

Concept

Determine the transformation or sequence of transformations that maps one figure onto another.

Rules

1. Look at the polygon on the left.
2. Determine which transformation(s) would need to be made to map the figure on the left to the figure on the right.
Translation: A translation slides a figure from one position to another without turning it.
Reflection: A transformation where a figure is flipped over a line called a line of reflection.
Rotation: A rotation is a transformation in which a figure is rotated, or turned, about a fixed point.
Dilation: A transformation that enlarges or reduces a figure by a scale factor.

Example

Which transformation(s) would need to be made to map the figure on the left to the figure on the right?

Solution

If you take the image on the left and reflect it over a horizontal line we will end up with two trapezoids with the same orientation, sitting side by side. In order to map the trapezoid on the left to the one on the right, we would then need to translate it to the right and up. Both a reflection and translation are needed to map the figure on the left to the figure on the right.

Practice Reflections and Translations

Practice Problem 1

Use translation notation to describe the translation from point A to point A’.

Practice Problem 2

The fisherman is looking for fish to catch. Coordinate of fishermen is (5,9) and fish (3,-2). Use translation notation to describe the translation from the fisherman to the fish.

Practice Problem 3

Graph the reflection over the x-axis of the figure below.

Practice Problem 4

Olivia is painting geometric shapes. She painted only on the right side of the paper. On the left side, she wants to paint the exact reflection of the right side. Look at Olivia’s sketch below and plot the shapes.

Practice Problem 5

Triangle ABC has vertices A(-5,2), B(-2,1), and C(-2,4). Triangle ABC is reflected over the y-axis and translated 1 unit down. What are the coordinates of the vertices of triangle A’B’C’?